A shipment of 1500 heads of cabbage each of which was approximately the same size was purchased for $600. The day the shipment arrived 2/3 heads were sold, each at 25 percent above the cost per head. The following day the rest were sold at the price per head equal to the 10 percent less than the price each head sold for one day before. What was the gross profit on this shipment?
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Gross Profit Word Problem
Source: Beat The GMAT — Problem Solving |
-
indiantiger
- Master | Next Rank: 500 Posts
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Here is how I would approach the problem :
Given :
Total number of product = 1500
total purchase price = 600
purchase price per cabbage head = 600/1500 = 6/15 = 2/5
Gross profit = selling price - purchase price
selling price = cabbage sold on first day + cabbage sold the next day
cabbage sold on first day = 2/3*1500 * {2/5 +2/5*1/4}=1000 *2/5(5/4)
=1000*1/2
= 500
cabbage sold on next day = 1/3*1500 *{2/5-2/5*1/10} = 500 {2/5(9/10)} = 10*18
= 180
total selling price of cabbage = 500+180 = 680
gross profit = 680-600 = 80(whats the OA?)
I hope this helps.
Given :
Total number of product = 1500
total purchase price = 600
purchase price per cabbage head = 600/1500 = 6/15 = 2/5
Gross profit = selling price - purchase price
selling price = cabbage sold on first day + cabbage sold the next day
cabbage sold on first day = 2/3*1500 * {2/5 +2/5*1/4}=1000 *2/5(5/4)
=1000*1/2
= 500
cabbage sold on next day = 1/3*1500 *{2/5-2/5*1/10} = 500 {2/5(9/10)} = 10*18
= 180
total selling price of cabbage = 500+180 = 680
gross profit = 680-600 = 80(whats the OA?)
I hope this helps.
-
indiantiger
- Master | Next Rank: 500 Posts
- Posts: 362
- Thanked: 26 times
slight mistake on my part for the second day sale it should be
= 1/2 - 1/2*1/0 (10% less than the last day's price)
= 1/2*9/10 = 9/20
total sale price for second day = 9/20*500 = 450/2 = 225
total gross profit = 500 + 225 -600 = 725-600 = 125
I hope this time not wrong.
= 1/2 - 1/2*1/0 (10% less than the last day's price)
= 1/2*9/10 = 9/20
total sale price for second day = 9/20*500 = 450/2 = 225
total gross profit = 500 + 225 -600 = 725-600 = 125
I hope this time not wrong.
-
thephoenix
- Legendary Member
- Posts: 1560
- Thanked: 137 times
$125
total=1500
cost=600
cost per head=600/1500=2/5
25% above--->5/4*(2/5)=1/2
2/3 of heads--->1000
cost=1000*2=500
10% less of one days back price=9/10*1/2=9/20
left quantity=500
cost=500*9/20=225
tot selling price=500+225=725
profit=125
total=1500
cost=600
cost per head=600/1500=2/5
25% above--->5/4*(2/5)=1/2
2/3 of heads--->1000
cost=1000*2=500
10% less of one days back price=9/10*1/2=9/20
left quantity=500
cost=500*9/20=225
tot selling price=500+225=725
profit=125
price of each cabbage=600/1500=$0.40
125 percent of each cabbage=$0.50
2/3 of 1500 cabage=1000. 1000 sold at 25 percent above the cost head...total price=1000*0.50=500
10 percent less than the price each head sold for one day before, means each cabbage will be sold for 0.45(0.9*$0.5)
hence total proice of remaining 500 cabbage is =500 * 0.45=225
hence total money earned by selling is $725
Gross profit = $125
125 percent of each cabbage=$0.50
2/3 of 1500 cabage=1000. 1000 sold at 25 percent above the cost head...total price=1000*0.50=500
10 percent less than the price each head sold for one day before, means each cabbage will be sold for 0.45(0.9*$0.5)
hence total proice of remaining 500 cabbage is =500 * 0.45=225
hence total money earned by selling is $725
Gross profit = $125
vrowland wrote:A shipment of 1500 heads of cabbage each of which was approximately the same size was purchased for $600. The day the shipment arrived 2/3 heads were sold, each at 25 percent above the cost per head. The following day the rest were sold at the price per head equal to the 10 percent less than the price each head sold for one day before. What was the gross profit on this shipment?
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